For all positive real numbers x, (xˆ2)-x≥0.

I don't think this is true since for instance x can equal 2/3 and (2/3)ˆ2-(2/3)=-2/9 which is not greater than or equal to 0. Am i wrong?

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- September 14th 2011, 06:36 PMAquameatwadQuick Proof on real numbers
For all positive real numbers x, (xˆ2)-x≥0.

I don't think this is true since for instance x can equal 2/3 and (2/3)ˆ2-(2/3)=-2/9 which is not greater than or equal to 0. Am i wrong? - September 14th 2011, 06:43 PMSudharakaRe: Quick Proof on real numbers
- September 14th 2011, 06:50 PMAquameatwadRe: Quick Proof on real numbers
I see, so is the original proof "For all positive real numbers x, (xˆ2)-x≥0. " is only correct if you set the parameter x≥1.

So the original statement is false since 2/3 is a positive real number, and (2/3)ˆ2-(2/3)=-2/9 which is not greater than or equal to 0. Correct? Just want to make sure whats in my head is correct. - September 14th 2011, 08:26 PMSudharakaRe: Quick Proof on real numbers
- September 14th 2011, 08:51 PMProve ItRe: Quick Proof on real numbers
- September 15th 2011, 04:05 AMHallsofIvyRe: Quick Proof on real numbers
S0mewhat simpler, I think:

if and only if both factors on the left have the same sigh. If , x> 0 and , so that is true. If , x< 1 so that is true. But if , x is positive while x- 1 is negative so it is not true.